Additionally, the above inference methods for bandit algorithms are asymptotically valid and typically require either a large experiment or a large batch size. As shown in Section , they may either fail to control type-I error (AW-AIPW in small samples), or have practically no power (i.e., \(<0.1\)  for BOLS in a batch size of 3 and regardless the sample size). Note that the BOLS is applicable only for batch sizes \(\ge 3\) . Existing valid inferential approaches for finite samples are also inefficient in terms of statistical power [1]}, [2]}. Thus, existing options for valid hypothesis testing for MAB collected data are applicable only to large experiments (and/or large batches), with a moderate reward performance and insufficient statistical power.
